Diesel engine fuel injection systems have been constructed in combination with a distributor unit to distribute the injected fuel to the respective cylinders; such combined Diesel engine distributor-injection pumps are described in the "Automotive Handbook", issued by the assignee of the present invention, in the chapter relating to Diesel engine injection pumps. Such pumps control the quantity of injected fuel as well as the timing of the injection. They include a speed-sensitive element, such as a centrifugal controller, which changes the injection instant with respect to the top-dead-center (TDC) position of the piston. Mechanical or mechanical/hydraulic adjustment arrangements are used. Play and backlash must be rigorously avoided in order to reduce erroneous injection timing and maladjustment. Thus, numerous precise fittings and matching engagement surfaces have to be carefully made; numerous accurately matched and fitted engagement surfaces between the various elements of the injection pumps are required. This causes expense and the overall transmission mechanism then likewise becomes expensive. Additional elements are required to permit correction under warm-up conditions.